MC145151–2 through MC145158–2
28
MOTOROLA
DESIGN CONSIDERATIONS
PHASE–LOCKED LOOP — LOW–PASS FILTER DESIGN
C)
_
+A
C
R2
C
VCO
C
VCO
R2
B)
A)
C
VCO
PDout
PDout
φ
R —
φ
V —
PDout —
φ
R
φ
V
R1
R1
R1
R1
R2
NOTE: Sometimes R1 is split into two series resistors, each R1
÷
2. A capacitor CC is then placed from the midpoint to ground to further
filter
φ
V and
φ
R. The value of CC should be such that the corner frequency of this network does not significantly affect
ω
n.
The
φ
R and
φ
V outputs swing rail–to–rail. Therefore, the user should be careful not to exceed the common mode input range of the
op amp used in the combiner/loop filter.
DEFINITIONS:
N = Total Division Ratio in feedback loop
K
φ
(Phase Detector Gain) = VDD/
4
π
for PDout
K
φ
(Phase Detector Gain) = VDD/2
π
for
φ
V and
φ
R
2
π
fVCO
VVCO
for a typical design wn (Natural Frequency)
≈
2
π
fr
Damping Factor:
ζ
1
KVCO (VCO Gain) =
10
(at phase detector input).
RECOMMENDED READING:
Gardner, Floyd M.,
Phaselock Techniques (second edition).
New York, Wiley–Interscience, 1979.
Manassewitsch, Vadim,
Frequency Synthesizers: Theory and Design (second edition).
New York, Wiley–Interscience, 1980.
Blanchard, Alain,
Phase–Locked Loops: Application to Coherent Receiver Design.
New York, Wiley–Interscience, 1976.
Egan, William F.,
Frequency Synthesis by Phase Lock.
New York, Wiley–Interscience, 1981.
Rohde, Ulrich L.,
Digital PLL Frequency Synthesizers Theory and Design.
Englewood Cliffs, NJ, Prentice–Hall, 1983.
Berlin, Howard M.,
Design of Phase–Locked Loop Circuits, with Experiments.
Indianapolis, Howard W. Sams and Co., 1978.
Kinley, Harold,
The PLL Synthesizer Cookbook.
Blue Ridge Summit, PA, Tab Books, 1980.
AN535, Phase–Locked Loop Design Fundamentals, Motorola Semiconductor Products, Inc., 1970.
AR254, Phase–Locked Loop Design Articles, Motorola Semiconductor Products, Inc., Reprinted with permission from
Electronic Design,
1987.
φ
R —
φ
V —
F(s) =
ASSUMING GAIN A IS VERY LARGE, THEN:
F(s) =
ζ
=
ω
n =
NR1C
R1sC + 1
ω
n =
ζ
=
ω
nR2C
2
R2sC + 1
R1sC
1
N
ω
n
2K
φ
KVCO
F(s) =
ζ
=
ω
n =
(R1+ R2)sC + 1
R2sC + 1
NC(R1 + R2)
R2C +
N
K
φ
KVCO
K
φ
KVCO
NCR1
0.5
ω
n
K
φ
KVCO
K
φ
KVCO